The Ghirlanda-Guerra identities for mixed p-spin model

We show that, under the conditions known to imply the validity of the Parisi formula, if the generic Sherrington-Kirkpatrick Hamiltonian contains a p-spin term then the Ghirlanda-Guerra identities for the pth power of the overlap hold in a strong sense without averaging. This implies strong version of the extended Ghirlanda-Guerra identities for mixed p-spin models than contain terms for all even p >= 2 and p = 1. (C) 2010 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.